Question

Chapter 6, Section 1-CI, Exercise 012 Use the normal distribution to find a confidence interval for a proportion given the relevant sample results. Give the best point estimate for , the margin of error, and the confidence interval. Assume the results come from a random sample. A 95% confidence interval for p given that p-hat = 0.9 and n = 120 . Round your answer for the point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places.

Point estimate: 0.9

Margin of Error:

Confidence Interval:

Answer 1

Solution :

Given that,

n = 120

Point estimate = sample proportion = = 0.9

= 1 - = 1 - 0.9 = 0.1

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.9 * 0.1) / 120)

= 0.054

A 95% confidence interval for population proportion p is ,

± E

0.9 ± 0.054

(0.846 , 0.954)